7. Two particles \(P\) and \(Q\), of masses \(2 m\) and \(3 m\) respectively, are connected by a light string. Initially, \(P\) is at rest on a smooth horizontal table. The string passes over a small smooth pulley and \(Q\) rests on a rough plane inclined at an
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angle \(\theta\) to the horizontal, where \(\tan \theta = \frac { 4 } { 3 }\). The coefficient of friction between \(Q\) and the inclined plane is \(\frac { 1 } { 6 }\).
The system is released from rest with \(Q\) at a distance of 0.8 metres above a horizontal floor.

1. Show that the acceleration of \(P\) and \(Q\) is \(\frac { 21 g } { 50 }\), stating a modelling assumption which you must make to ensure that both particles have the same acceleration.
2. Find the speed with which \(Q\) hits the floor. After \(Q\) hits the floor and does not rebound, \(P\) moves a further 0.2 m until it hits the pulley.
3. Find the total time after the system is released before \(P\) hits the pulley.